Abstract:
Non-equilibrium black hole horizons are considered in scaling theories
with generic Lifshitz invariance and an unbroken U(1) symmetry.
There is also a special form of hyperscaling violation
associated with a non-trivial conduction exponent.
The boundary stress tensor is computed and renormalized,
and the associated hydrodynamic equations are derived.
Upon a non-trivial redefinition of boundary sources associated with the
U(1) gauge field,
the equations are mapped to the standard non-relativistic hydrodynamics
equations
coupled to a mass current and an external Newton potentials.
The shear viscosity to entropy ratio is the same as in the relativistic
case.